# Rendiconti del Seminario Matematico della Università di Padova

Full-Text PDF (242 KB) | Metadata | Table of Contents | RSMUP summary

**Volume 139, 2018, pp. 261–281**

**DOI: 10.4171/RSMUP/139-11**

Published online: 2018-06-06

Nunke’s problem for abelian $p$-groups of uncountable length

Patrick W. Keef^{[1]}(1) Whitman College, Walla Walla, USA

*Nunke's problem* asks when the torsion product of two abelian $p$-groups is a direct sum of countable reduced groups. In previous work the author gave a complete answer to this question when the groups involved have countable length. In this paper a complete answer is given in the case of groups of uncountable length, at least in any set-theoretic universe in which $2^{\aleph_1}=\aleph_2$.

*Keywords: *Nunke’s problem, abelian $p$-groups, dsc groups

Keef Patrick: Nunke’s problem for abelian $p$-groups of uncountable length. *Rend. Sem. Mat. Univ. Padova* 139 (2018), 261-281. doi: 10.4171/RSMUP/139-11